Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_76

2/76 A projectile is ejected into an experimental fluid at time \( t = 0 \). The initial speed is \( v_0 \) and the angle to the horizontal is \( \theta \). The drag on the projectile results in an acceleration term \( \mathbf{a}_D = -k\mathbf{v} \), where \( k \) is a constant and \( \mathbf{v} \) is the velocity of the projectile. Determine the \( x \)- and \( y \)-components of both the velocity and displacement as functions of time. What is the terminal velocity? Include the effects of gravitational acceleration.